Self-Driving Car Engineer Nanodegree

Deep Learning

Project: Build a Traffic Sign Recognition Classifier

In this notebook, a template is provided for you to implement your functionality in stages, which is required to successfully complete this project. If additional code is required that cannot be included in the notebook, be sure that the Python code is successfully imported and included in your submission if necessary.

Note: Once you have completed all of the code implementations, you need to finalize your work by exporting the iPython Notebook as an HTML document. Before exporting the notebook to html, all of the code cells need to have been run so that reviewers can see the final implementation and output. You can then export the notebook by using the menu above and navigating to \n", "File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.

In addition to implementing code, there is a writeup to complete. The writeup should be completed in a separate file, which can be either a markdown file or a pdf document. There is a write up template that can be used to guide the writing process. Completing the code template and writeup template will cover all of the rubric points for this project.

The rubric contains "Stand Out Suggestions" for enhancing the project beyond the minimum requirements. The stand out suggestions are optional. If you decide to pursue the "stand out suggestions", you can include the code in this Ipython notebook and also discuss the results in the writeup file.

Note: Code and Markdown cells can be executed using the Shift + Enter keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.


Step 0: Load The Data

In [1]:
# Load pickled data
import pickle

# TODO: Fill this in based on where you saved the training and testing data

training_file = 'traffic-signs-data/train.p'
validation_file = 'traffic-signs-data/valid.p'
testing_file = 'traffic-signs-data/test.p'

with open(training_file, mode='rb') as f:
    train = pickle.load(f)
with open(validation_file, mode='rb') as f:
    valid = pickle.load(f)
with open(testing_file, mode='rb') as f:
    test = pickle.load(f)
    
X_train, y_train = train['features'], train['labels']
X_valid, y_valid = valid['features'], valid['labels']
X_test, y_test = test['features'], test['labels']

Step 1: Dataset Summary & Exploration

The pickled data is a dictionary with 4 key/value pairs:

  • 'features' is a 4D array containing raw pixel data of the traffic sign images, (num examples, width, height, channels).
  • 'labels' is a 1D array containing the label/class id of the traffic sign. The file signnames.csv contains id -> name mappings for each id.
  • 'sizes' is a list containing tuples, (width, height) representing the original width and height the image.
  • 'coords' is a list containing tuples, (x1, y1, x2, y2) representing coordinates of a bounding box around the sign in the image. THESE COORDINATES ASSUME THE ORIGINAL IMAGE. THE PICKLED DATA CONTAINS RESIZED VERSIONS (32 by 32) OF THESE IMAGES

Complete the basic data summary below. Use python, numpy and/or pandas methods to calculate the data summary rather than hard coding the results. For example, the pandas shape method might be useful for calculating some of the summary results.

Provide a Basic Summary of the Data Set Using Python, Numpy and/or Pandas

In [2]:
### Replace each question mark with the appropriate value. 
### Use python, pandas or numpy methods rather than hard coding the results
import numpy as np

# TODO: Number of training examples
n_train = len(X_train)

# TODO: Number of validation examples
n_validation = len(X_valid)

# TODO: Number of testing examples.
n_test = len(X_test)

# TODO: What's the shape of an traffic sign image?
image_shape = X_train[0].shape

# TODO: How many unique classes/labels there are in the dataset.
n_classes = len(np.unique(y_train))

print("Number of training examples =", n_train)
print("Number of validation examples =", n_validation)
print("Number of testing examples =", n_test)
print("Image data shape =", image_shape)
print("Number of classes =", n_classes)
Number of training examples = 34799
Number of validation examples = 4410
Number of testing examples = 12630
Image data shape = (32, 32, 3)
Number of classes = 43

Include an exploratory visualization of the dataset

Visualize the German Traffic Signs Dataset using the pickled file(s). This is open ended, suggestions include: plotting traffic sign images, plotting the count of each sign, etc.

The Matplotlib examples and gallery pages are a great resource for doing visualizations in Python.

NOTE: It's recommended you start with something simple first. If you wish to do more, come back to it after you've completed the rest of the sections. It can be interesting to look at the distribution of classes in the training, validation and test set. Is the distribution the same? Are there more examples of some classes than others?

In [3]:
### Data exploration visualization code goes here.
### Feel free to use as many code cells as needed.
import csv
import random
import matplotlib.pyplot as plt
# Visualizations will be shown in the notebook.
%matplotlib inline

# Read the Sign Names from the CSV File
with open('signnames.csv') as f_csv:
    reader = csv.reader(f_csv)
    next (reader) # skip header
    signnames = [r for r in reader]

# Show 4 Random Images of each type of sign
fig, ax = plt.subplots(n_classes, 4, figsize=(25,140))
labels, indexes, counts = np.unique(y_train, return_index=True, return_counts = True)

for c in range(n_classes):
    images = X_train[indexes[c]:indexes[c]+counts[c]]
    for img in range(4):
        index = random.randint(0, len(images)-1)
        ax[c][img].imshow(images[index])
        ax[c][img].set_title(signnames[c][1])

plt.subplots_adjust(hspace=0.3)
plt.show()

Step 2: Design and Test a Model Architecture

Design and implement a deep learning model that learns to recognize traffic signs. Train and test your model on the German Traffic Sign Dataset.

The LeNet-5 implementation shown in the classroom at the end of the CNN lesson is a solid starting point. You'll have to change the number of classes and possibly the preprocessing, but aside from that it's plug and play!

With the LeNet-5 solution from the lecture, you should expect a validation set accuracy of about 0.89. To meet specifications, the validation set accuracy will need to be at least 0.93. It is possible to get an even higher accuracy, but 0.93 is the minimum for a successful project submission.

There are various aspects to consider when thinking about this problem:

  • Neural network architecture (is the network over or underfitting?)
  • Play around preprocessing techniques (normalization, rgb to grayscale, etc)
  • Number of examples per label (some have more than others).
  • Generate fake data.

Here is an example of a published baseline model on this problem. It's not required to be familiar with the approach used in the paper but, it's good practice to try to read papers like these.

Pre-process the Data Set (normalization, grayscale, etc.)

Minimally, the image data should be normalized so that the data has mean zero and equal variance. For image data, (pixel - 128)/ 128 is a quick way to approximately normalize the data and can be used in this project.

Other pre-processing steps are optional. You can try different techniques to see if it improves performance.

Use the code cell (or multiple code cells, if necessary) to implement the first step of your project.

In [4]:
### Preprocess the data here. It is required to normalize the data. Other preprocessing steps could include 
### converting to grayscale, etc.
### Feel free to use as many code cells as needed.

import cv2

# convert to grayscale
def grayscale(image):
    return cv2.cvtColor(image, cv2.COLOR_RGB2GRAY)

def equalize(image):
    return cv2.equalizeHist(image)

def normalize(image):
    min, max = np.min(image), np.max(image)
    return (image - min) / (max - min) * 2 - 1

def preprocess_image(image):
    return np.expand_dims(normalize(equalize(grayscale(image))), axis=2)

def preprocess(dataset):
    return np.array([preprocess_image(image) for image in dataset])

X_train_n = preprocess(X_train)
X_valid_n = preprocess(X_valid)
X_test_n = preprocess(X_test)

Visualize Pre-process Images

In [5]:
A4_PORTRAIT = (8.27, 11.69)
A4_LANDSCAPE = A4_PORTRAIT[::-1]

f, axes = plt.subplots(11, 4)
f.set_size_inches(A4_PORTRAIT)
c = 0
for row in axes:
    for ax in row:
        if c < n_classes:
            im = (X_train_n[np.random.choice(np.where(y_train == c)[0], 1)] + 1) / 2
            ax.imshow(im[0,:,:,0], cmap='gray')
        ax.grid(False)
        ax.axis('off')
        c += 1
plt.show()

Data Augumentation

In [6]:
from tqdm import tqdm

def rotate(image, angle=15):
    angle = np.random.randint(-angle, angle)
    M = cv2.getRotationMatrix2D((16, 16), angle, 1)
    return cv2.warpAffine(src=image, M=M, dsize=(32, 32))

def translate(image, pixels=2):
    tx = np.random.choice(range(-pixels, pixels))
    ty = np.random.choice(range(-pixels, pixels))
    M = np.float32([[1, 0, tx], [0, 1, ty]])
    return cv2.warpAffine(src=image, M=M, dsize=(32, 32))

def random_bright(image):
    eff = 0.5 + np.random.random()
    return image * eff

def generate(images, count):
    generated = []
    while True:
        for image in images:
            if len(generated) == count:
                return generated
            image = random_bright(image)
            image = rotate(image)
            image = translate(image)
            image = normalize(image)
            generated.append(np.expand_dims(image, axis=2))

unique, counts = np.unique(y_train, return_counts=True)

target = 5000
x_augmented = []
y_augmented = []

for cls, count in tqdm(list(zip(unique, counts)), 'Augmenting training dataset'):
    diff = target - count
    x_augmented += generate(X_train_n[np.where(y_train == cls)[0]], diff)
    y_augmented += [cls for _ in range(diff)]

X_train_n = np.concatenate([X_train_n, np.array(x_augmented)])
y_train = np.concatenate([y_train, np.array(y_augmented)])
n_train = y_train.size
print('Final number of training examples', n_train)
Augmenting training dataset: 100%|██████████| 43/43 [00:16<00:00,  2.66it/s]
Final number of training examples 215000

Model Architecture

In [7]:
### Define your architecture here.
### Feel free to use as many code cells as needed.

import tensorflow as tf
from tensorflow.contrib.layers import flatten

conv1_activation = None

def LeNet(x):
    global conv1_activation
    
    # Arguments used for tf.truncated_normal, randomly defines variables for the weights and biases for each layer
    mu = 0
    sigma = 0.1
    
    # SOLUTION: Layer 1: Convolutional. Input = 32x32x1. Output = 28x28x6.
    conv1_W = tf.Variable(tf.truncated_normal(shape=(5, 5, 1, 6), mean = mu, stddev = sigma))
    conv1_b = tf.Variable(tf.zeros(6))
    conv1   = tf.nn.conv2d(x, conv1_W, strides=[1, 1, 1, 1], padding='VALID') + conv1_b

    # SOLUTION: Activation.
    conv1_activation = conv1 = tf.nn.relu(conv1)

    # SOLUTION: Pooling. Input = 28x28x6. Output = 14x14x6.
    conv1 = tf.nn.max_pool(conv1, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='VALID')

    # SOLUTION: Layer 2: Convolutional. Output = 10x10x16.
    conv2_W = tf.Variable(tf.truncated_normal(shape=(5, 5, 6, 16), mean = mu, stddev = sigma))
    conv2_b = tf.Variable(tf.zeros(16))
    conv2   = tf.nn.conv2d(conv1, conv2_W, strides=[1, 1, 1, 1], padding='VALID') + conv2_b
    
    # SOLUTION: Activation.
    conv2 = tf.nn.relu(conv2)

    # SOLUTION: Pooling. Input = 10x10x16. Output = 5x5x16.
    conv2 = tf.nn.max_pool(conv2, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='VALID')

    # SOLUTION: Flatten. Input = 5x5x16. Output = 400.
    fc0   = flatten(conv2)
    
    # SOLUTION: Layer 3: Fully Connected. Input = 400. Output = 120.
    fc1_W = tf.Variable(tf.truncated_normal(shape=(400, 120), mean = mu, stddev = sigma))
    fc1_b = tf.Variable(tf.zeros(120))
    fc1   = tf.matmul(fc0, fc1_W) + fc1_b
    
    # SOLUTION: Activation.
    fc1    = tf.nn.relu(fc1)
    
    fc1  = tf.nn.dropout(fc1, keep_prob)

    # SOLUTION: Layer 4: Fully Connected. Input = 120. Output = 84.
    fc2_W  = tf.Variable(tf.truncated_normal(shape=(120, 84), mean = mu, stddev = sigma))
    fc2_b  = tf.Variable(tf.zeros(84))
    fc2    = tf.matmul(fc1, fc2_W) + fc2_b
    
    # SOLUTION: Activation.
    fc2    = tf.nn.relu(fc2)
    
    fc2    = tf.nn.dropout(fc2, keep_prob)

    # SOLUTION: Layer 5: Fully Connected. Input = 84. Output = 43.
    fc3_W  = tf.Variable(tf.truncated_normal(shape=(84, 43), mean = mu, stddev = sigma))
    fc3_b  = tf.Variable(tf.zeros(43))
    logits = tf.matmul(fc2, fc3_W) + fc3_b
    
    return logits

Train, Validate and Test the Model

A validation set can be used to assess how well the model is performing. A low accuracy on the training and validation sets imply underfitting. A high accuracy on the training set but low accuracy on the validation set implies overfitting.

In [8]:
### Train your model here.
### Calculate and report the accuracy on the training and validation set.
### Once a final model architecture is selected, 
### the accuracy on the test set should be calculated and reported as well.
### Feel free to use as many code cells as needed.
from sklearn.utils import shuffle

x = tf.placeholder(tf.float32, (None, 32, 32, 1))
y = tf.placeholder(tf.int32, (None))
keep_prob = tf.placeholder(tf.float32) 
one_hot_y = tf.one_hot(y, 43)

rate = 0.001
EPOCHS = 50
BATCH_SIZE = 128

logits = LeNet(x)
cross_entropy = tf.nn.softmax_cross_entropy_with_logits(logits=logits, labels=one_hot_y)
loss_operation = tf.reduce_mean(cross_entropy)
optimizer = tf.train.AdamOptimizer(learning_rate = rate)
training_operation = optimizer.minimize(loss_operation)

correct_prediction = tf.equal(tf.argmax(logits, 1), tf.argmax(one_hot_y, 1))
accuracy_operation = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
saver = tf.train.Saver()

def evaluate(X_data, y_data):
    num_examples = len(X_data)
    total_accuracy = 0
    sess = tf.get_default_session()
    for offset in range(0, num_examples, BATCH_SIZE):
        batch_x, batch_y = X_data[offset:offset+BATCH_SIZE], y_data[offset:offset+BATCH_SIZE]
        accuracy = sess.run(accuracy_operation, feed_dict={x: batch_x, y: batch_y, keep_prob: 1.0})
        total_accuracy += (accuracy * len(batch_x))
    return total_accuracy / num_examples

model_name = './lenet'
history = []

with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    num_examples = len(X_train_n)
    
    print("Training...")
    print()
    for i in range(EPOCHS):
        X_train_n, y_train = shuffle(X_train_n, y_train)
        for offset in range(0, num_examples, BATCH_SIZE):
            end = offset + BATCH_SIZE
            batch_x, batch_y = X_train_n[offset:end], y_train[offset:end]
            sess.run(training_operation, feed_dict={x: batch_x, y: batch_y, keep_prob: 0.5})
        
        training_accuracy = evaluate(X_train_n, y_train)
        validation_accuracy = evaluate(X_valid_n, y_valid)
        test_accuracy = evaluate(X_test_n, y_test)
        history.append([training_accuracy, validation_accuracy, test_accuracy])
        print("EPOCH {} ...".format(i+1))
        print("Training Accuracy = {:.3f}".format(training_accuracy))
        print("Validation Accuracy = {:.3f}".format(validation_accuracy))
        print("Test Accuracy = {:.3f}".format(test_accuracy))
        print()
        
    saver.save(sess, model_name)
    print("Model saved")
Training...

EPOCH 1 ...
Training Accuracy = 0.869
Validation Accuracy = 0.864
Test Accuracy = 0.844

EPOCH 2 ...
Training Accuracy = 0.927
Validation Accuracy = 0.924
Test Accuracy = 0.902

EPOCH 3 ...
Training Accuracy = 0.950
Validation Accuracy = 0.941
Test Accuracy = 0.917

EPOCH 4 ...
Training Accuracy = 0.958
Validation Accuracy = 0.951
Test Accuracy = 0.923

EPOCH 5 ...
Training Accuracy = 0.968
Validation Accuracy = 0.956
Test Accuracy = 0.928

EPOCH 6 ...
Training Accuracy = 0.974
Validation Accuracy = 0.959
Test Accuracy = 0.937

EPOCH 7 ...
Training Accuracy = 0.972
Validation Accuracy = 0.965
Test Accuracy = 0.938

EPOCH 8 ...
Training Accuracy = 0.979
Validation Accuracy = 0.968
Test Accuracy = 0.945

EPOCH 9 ...
Training Accuracy = 0.978
Validation Accuracy = 0.966
Test Accuracy = 0.940

EPOCH 10 ...
Training Accuracy = 0.980
Validation Accuracy = 0.963
Test Accuracy = 0.944

EPOCH 11 ...
Training Accuracy = 0.982
Validation Accuracy = 0.970
Test Accuracy = 0.942

EPOCH 12 ...
Training Accuracy = 0.982
Validation Accuracy = 0.974
Test Accuracy = 0.944

EPOCH 13 ...
Training Accuracy = 0.985
Validation Accuracy = 0.971
Test Accuracy = 0.943

EPOCH 14 ...
Training Accuracy = 0.985
Validation Accuracy = 0.972
Test Accuracy = 0.943

EPOCH 15 ...
Training Accuracy = 0.986
Validation Accuracy = 0.971
Test Accuracy = 0.945

EPOCH 16 ...
Training Accuracy = 0.984
Validation Accuracy = 0.965
Test Accuracy = 0.942

EPOCH 17 ...
Training Accuracy = 0.985
Validation Accuracy = 0.971
Test Accuracy = 0.946

EPOCH 18 ...
Training Accuracy = 0.988
Validation Accuracy = 0.975
Test Accuracy = 0.943

EPOCH 19 ...
Training Accuracy = 0.988
Validation Accuracy = 0.976
Test Accuracy = 0.946

EPOCH 20 ...
Training Accuracy = 0.988
Validation Accuracy = 0.975
Test Accuracy = 0.948

EPOCH 21 ...
Training Accuracy = 0.989
Validation Accuracy = 0.978
Test Accuracy = 0.949

EPOCH 22 ...
Training Accuracy = 0.989
Validation Accuracy = 0.978
Test Accuracy = 0.953

EPOCH 23 ...
Training Accuracy = 0.988
Validation Accuracy = 0.971
Test Accuracy = 0.947

EPOCH 24 ...
Training Accuracy = 0.990
Validation Accuracy = 0.981
Test Accuracy = 0.951

EPOCH 25 ...
Training Accuracy = 0.989
Validation Accuracy = 0.976
Test Accuracy = 0.949

EPOCH 26 ...
Training Accuracy = 0.988
Validation Accuracy = 0.975
Test Accuracy = 0.947

EPOCH 27 ...
Training Accuracy = 0.989
Validation Accuracy = 0.973
Test Accuracy = 0.944

EPOCH 28 ...
Training Accuracy = 0.990
Validation Accuracy = 0.982
Test Accuracy = 0.953

EPOCH 29 ...
Training Accuracy = 0.991
Validation Accuracy = 0.978
Test Accuracy = 0.952

EPOCH 30 ...
Training Accuracy = 0.991
Validation Accuracy = 0.980
Test Accuracy = 0.949

EPOCH 31 ...
Training Accuracy = 0.991
Validation Accuracy = 0.977
Test Accuracy = 0.949

EPOCH 32 ...
Training Accuracy = 0.991
Validation Accuracy = 0.981
Test Accuracy = 0.953

EPOCH 33 ...
Training Accuracy = 0.990
Validation Accuracy = 0.979
Test Accuracy = 0.948

EPOCH 34 ...
Training Accuracy = 0.991
Validation Accuracy = 0.978
Test Accuracy = 0.953

EPOCH 35 ...
Training Accuracy = 0.990
Validation Accuracy = 0.976
Test Accuracy = 0.948

EPOCH 36 ...
Training Accuracy = 0.992
Validation Accuracy = 0.984
Test Accuracy = 0.953

EPOCH 37 ...
Training Accuracy = 0.990
Validation Accuracy = 0.975
Test Accuracy = 0.946

EPOCH 38 ...
Training Accuracy = 0.991
Validation Accuracy = 0.981
Test Accuracy = 0.951

EPOCH 39 ...
Training Accuracy = 0.992
Validation Accuracy = 0.981
Test Accuracy = 0.950

EPOCH 40 ...
Training Accuracy = 0.991
Validation Accuracy = 0.980
Test Accuracy = 0.953

EPOCH 41 ...
Training Accuracy = 0.993
Validation Accuracy = 0.981
Test Accuracy = 0.949

EPOCH 42 ...
Training Accuracy = 0.993
Validation Accuracy = 0.983
Test Accuracy = 0.953

EPOCH 43 ...
Training Accuracy = 0.992
Validation Accuracy = 0.980
Test Accuracy = 0.950

EPOCH 44 ...
Training Accuracy = 0.993
Validation Accuracy = 0.979
Test Accuracy = 0.954

EPOCH 45 ...
Training Accuracy = 0.993
Validation Accuracy = 0.985
Test Accuracy = 0.954

EPOCH 46 ...
Training Accuracy = 0.992
Validation Accuracy = 0.983
Test Accuracy = 0.952

EPOCH 47 ...
Training Accuracy = 0.991
Validation Accuracy = 0.981
Test Accuracy = 0.951

EPOCH 48 ...
Training Accuracy = 0.991
Validation Accuracy = 0.981
Test Accuracy = 0.951

EPOCH 49 ...
Training Accuracy = 0.993
Validation Accuracy = 0.982
Test Accuracy = 0.952

EPOCH 50 ...
Training Accuracy = 0.992
Validation Accuracy = 0.981
Test Accuracy = 0.951

Model saved
In [9]:
def plot_history(history, modelname):
    plt.figure(figsize=A4_LANDSCAPE)
    plt.title('Model training history: {}'.format(modelname))
    plt.plot(range(1, EPOCHS+1), history)
    plt.legend(['Training', 'Validation', 'Test'])
    plt.xlabel('Epoch')
    plt.ylabel('Accuracy')
    plt.xlim([1, EPOCHS])
    plt.show()

plot_history(history, model_name)

Step 3: Test a Model on New Images

To give yourself more insight into how your model is working, download at least five pictures of German traffic signs from the web and use your model to predict the traffic sign type.

You may find signnames.csv useful as it contains mappings from the class id (integer) to the actual sign name.

Load and Output the Images

In [10]:
### Load the images and plot them here.
### Feel free to use as many code cells as needed.

import os
import matplotlib.image as mpimg

test_images_in = np.array([], dtype=np.uint8).reshape(0, 32, 32, 3)
test_labels = np.array([18, 17, 25, 1, 14])

files = os.listdir('test_images/')
files.sort()
fig,ax=plt.subplots(1, 5, figsize=(15, 8), squeeze=True)
ax = ax.ravel()

for item in range(len(files)):
    image = mpimg.imread('test_images/' + files[item])
    resized = cv2.resize(image,(32, 32))
    ax[item].imshow(resized)
    ax[item].set_title(files[item])
    test_images_in = np.concatenate((test_images_in, np.expand_dims(resized, 0)), axis=0)

test_images_in = np.array(test_images_in)
test_images_n = preprocess(test_images_in)
print('test_images_n.shape = ' + str(test_images_n.shape))
test_images_n.shape = (5, 32, 32, 1)

Predict the Sign Type for Each Image

In [11]:
### Run the predictions here and use the model to output the prediction for each image.
### Make sure to pre-process the images with the same pre-processing pipeline used earlier.
### Feel free to use as many code cells as needed.

with tf.Session() as sess:
        saver.restore(sess, tf.train.latest_checkpoint('.'))
        predictions = sess.run(tf.argmax(logits, 1), feed_dict={x: test_images_n, keep_prob: 1.0})

print('\n[Predict the Sign Type for Each Image]')
for (test_label, prediction) in zip(test_labels, predictions):
    result = 'PASS' if test_label == prediction else 'FAIL'
    print('result = ' + result + ', test_label = ' + str(test_label) + ', prediction = ' + str(prediction))
INFO:tensorflow:Restoring parameters from ./lenet

[Predict the Sign Type for Each Image]
result = PASS, test_label = 18, prediction = 18
result = PASS, test_label = 17, prediction = 17
result = PASS, test_label = 25, prediction = 25
result = PASS, test_label = 1, prediction = 1
result = PASS, test_label = 14, prediction = 14

Analyze Performance

In [12]:
### Calculate the accuracy for these 5 new images. 
### For example, if the model predicted 1 out of 5 signs correctly, it's 20% accurate on these new images.

with tf.Session() as sess:
    saver.restore(sess, tf.train.latest_checkpoint('.'))
    test_accuracy = evaluate(test_images_n, test_labels)
    print("Test Accuracy(new images) = {:.3f}".format(test_accuracy))
INFO:tensorflow:Restoring parameters from ./lenet
Test Accuracy(new images) = 1.000

Output Top 5 Softmax Probabilities For Each Image Found on the Web

For each of the new images, print out the model's softmax probabilities to show the certainty of the model's predictions (limit the output to the top 5 probabilities for each image). tf.nn.top_k could prove helpful here.

The example below demonstrates how tf.nn.top_k can be used to find the top k predictions for each image.

tf.nn.top_k will return the values and indices (class ids) of the top k predictions. So if k=3, for each sign, it'll return the 3 largest probabilities (out of a possible 43) and the correspoding class ids.

Take this numpy array as an example. The values in the array represent predictions. The array contains softmax probabilities for five candidate images with six possible classes. tf.nn.top_k is used to choose the three classes with the highest probability:

# (5, 6) array
a = np.array([[ 0.24879643,  0.07032244,  0.12641572,  0.34763842,  0.07893497,
         0.12789202],
       [ 0.28086119,  0.27569815,  0.08594638,  0.0178669 ,  0.18063401,
         0.15899337],
       [ 0.26076848,  0.23664738,  0.08020603,  0.07001922,  0.1134371 ,
         0.23892179],
       [ 0.11943333,  0.29198961,  0.02605103,  0.26234032,  0.1351348 ,
         0.16505091],
       [ 0.09561176,  0.34396535,  0.0643941 ,  0.16240774,  0.24206137,
         0.09155967]])

Running it through sess.run(tf.nn.top_k(tf.constant(a), k=3)) produces:

TopKV2(values=array([[ 0.34763842,  0.24879643,  0.12789202],
       [ 0.28086119,  0.27569815,  0.18063401],
       [ 0.26076848,  0.23892179,  0.23664738],
       [ 0.29198961,  0.26234032,  0.16505091],
       [ 0.34396535,  0.24206137,  0.16240774]]), indices=array([[3, 0, 5],
       [0, 1, 4],
       [0, 5, 1],
       [1, 3, 5],
       [1, 4, 3]], dtype=int32))

Looking just at the first row we get [ 0.34763842, 0.24879643, 0.12789202], you can confirm these are the 3 largest probabilities in a. You'll also notice [3, 0, 5] are the corresponding indices.

In [13]:
### Print out the top five softmax probabilities for the predictions on the German traffic sign images found on the web. 
### Feel free to use as many code cells as needed.

with tf.Session() as sess:
    saver.restore(sess, tf.train.latest_checkpoint('.'))
    top_k_outputs = sess.run(tf.nn.top_k(tf.nn.softmax(logits), k=5), feed_dict={x: test_images_n, keep_prob: 1.0})

print(top_k_outputs.values)
print()
print(top_k_outputs.indices)
INFO:tensorflow:Restoring parameters from ./lenet
[[  1.00000000e+00   7.01177874e-12   3.46768413e-25   2.88710889e-25
    2.91583627e-29]
 [  9.99989629e-01   7.29284375e-06   2.32902880e-06   6.80126675e-07
    4.36696617e-08]
 [  1.00000000e+00   4.48092882e-11   4.07605633e-12   2.07168961e-12
    6.05675441e-15]
 [  9.53960657e-01   4.60204259e-02   1.05691670e-05   8.40811663e-06
    2.41422757e-08]
 [  9.99975204e-01   2.26852153e-05   1.15858052e-06   9.77626087e-07
    2.25386501e-08]]

[[18 26 22 24 15]
 [17 38 14 13 16]
 [25 22 31 20 24]
 [ 1  2  5  4  7]
 [14 13  3 15 38]]

Project Writeup

Once you have completed the code implementation, document your results in a project writeup using this template as a guide. The writeup can be in a markdown or pdf file.

Note: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to \n", "File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.


Step 4 (Optional): Visualize the Neural Network's State with Test Images

This Section is not required to complete but acts as an additional excersise for understaning the output of a neural network's weights. While neural networks can be a great learning device they are often referred to as a black box. We can understand what the weights of a neural network look like better by plotting their feature maps. After successfully training your neural network you can see what it's feature maps look like by plotting the output of the network's weight layers in response to a test stimuli image. From these plotted feature maps, it's possible to see what characteristics of an image the network finds interesting. For a sign, maybe the inner network feature maps react with high activation to the sign's boundary outline or to the contrast in the sign's painted symbol.

Provided for you below is the function code that allows you to get the visualization output of any tensorflow weight layer you want. The inputs to the function should be a stimuli image, one used during training or a new one you provided, and then the tensorflow variable name that represents the layer's state during the training process, for instance if you wanted to see what the LeNet lab's feature maps looked like for it's second convolutional layer you could enter conv2 as the tf_activation variable.

For an example of what feature map outputs look like, check out NVIDIA's results in their paper End-to-End Deep Learning for Self-Driving Cars in the section Visualization of internal CNN State. NVIDIA was able to show that their network's inner weights had high activations to road boundary lines by comparing feature maps from an image with a clear path to one without. Try experimenting with a similar test to show that your trained network's weights are looking for interesting features, whether it's looking at differences in feature maps from images with or without a sign, or even what feature maps look like in a trained network vs a completely untrained one on the same sign image.

Combined Image

Your output should look something like this (above)

In [14]:
### Visualize your network's feature maps here.
### Feel free to use as many code cells as needed.

# image_input: the test image being fed into the network to produce the feature maps
# tf_activation: should be a tf variable name used during your training procedure that represents the calculated state of a specific weight layer
# activation_min/max: can be used to view the activation contrast in more detail, by default matplot sets min and max to the actual min and max values of the output
# plt_num: used to plot out multiple different weight feature map sets on the same block, just extend the plt number for each new feature map entry

def outputFeatureMap(image_input, tf_activation, activation_min=-1, activation_max=-1 ,plt_num=1):
    # Here make sure to preprocess your image_input in a way your network expects
    # with size, normalization, ect if needed
    # image_input =
    # Note: x should be the same name as your network's tensorflow data placeholder variable
    # If you get an error tf_activation is not defined it may be having trouble accessing the variable from inside a function
    activation = tf_activation.eval(session=sess,feed_dict={x : image_input})
    featuremaps = activation.shape[3]
    plt.figure(plt_num, figsize=(15,15))
    for featuremap in range(featuremaps):
        plt.subplot(6,8, featuremap+1) # sets the number of feature maps to show on each row and column
        plt.title('FeatureMap ' + str(featuremap)) # displays the feature map number
        if activation_min != -1 & activation_max != -1:
            plt.imshow(activation[0,:,:, featuremap], interpolation="nearest", vmin =activation_min, vmax=activation_max, cmap="gray")
        elif activation_max != -1:
            plt.imshow(activation[0,:,:, featuremap], interpolation="nearest", vmax=activation_max, cmap="gray")
        elif activation_min !=-1:
            plt.imshow(activation[0,:,:, featuremap], interpolation="nearest", vmin=activation_min, cmap="gray")
        else:
            plt.imshow(activation[0,:,:, featuremap], interpolation="nearest", cmap="gray")

# Visualize FeatureMap
for test_image_in, test_image_n in zip(test_images_in, test_images_n):
    with tf.Session() as sess:
        saver.restore(sess, tf.train.latest_checkpoint('.'))
        image_in = np.copy(test_image_in.squeeze())
        image_n = np.copy(test_image_n.squeeze())
        test_image = np.reshape(image_n, [1, 32, 32, 1], order='F')
        plt.figure(figsize=(2,2))
        plt.imshow(image_in, cmap="gray")
        plt.show()
        outputFeatureMap(test_image, conv1_activation, plt_num=1)
INFO:tensorflow:Restoring parameters from ./lenet
INFO:tensorflow:Restoring parameters from ./lenet
INFO:tensorflow:Restoring parameters from ./lenet
INFO:tensorflow:Restoring parameters from ./lenet
INFO:tensorflow:Restoring parameters from ./lenet